Why is there no displacement in height in the texture after adding the normal and height maps?
You are sending the vector into the Normal input of the shader. Using altered normals in materials by definition does not deform the mesh. To deform the mesh with a material, send the vector from a Displacement node into the Displacement input on the Output node, and set the material’s displacement mode to “Displacement only” or “Bump and displacement. Note that this will only work in Cycles, and will not generate new vertices: the mesh must be subdivided quite a bit for any noticeable effect.
To displace a mesh with a texture without using Cycles, use the Displacement modifier instead. Note that this will not generate new vertices, just like the last example.